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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A bank runs a 99% one-day VaR model and backtests it over 250 trading days. The 99% VaR is exceeded on 7 days. Under the Basel traffic-light approach for 250 observations, how many exceptions would the model be expected to produce on average if it were perfectly calibrated?

The expected number of exceptions is 2.5, found by multiplying 250 days by the 1% tail probability of a 99% VaR. The observed 7 exceptions exceed this expectation, which signals possible underestimation of risk by the model.

  1. A0.25
  2. B1.0
  3. C2.5Correct
  4. D7.0

Explanation

Expected exceptions = number of observations times the tail probability = 250 x 0.01 = 2.5. Seven exceptions is well above this, which suggests the model underestimates risk. Option 7.0 confuses the observed count with the expected count.

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